Some Dynamical Behavior of the Stuart-Landau Equation With a Periodic Excitation

CHEN Fang-qi; LIANG Jian-shu; CHEN Yu-shu

Volume 25 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(8): 796-800

Fan Xiu-chang. Using Generalized Variational Principles to Resolve the St. Venant’s Torsional Bar with a Crack[J]. Applied Mathematics and Mechanics, 1989, 10(2): 179-186.

Citation:

CHEN Fang-qi, LIANG Jian-shu, CHEN Yu-shu. Some Dynamical Behavior of the Stuart-Landau Equation With a Periodic Excitation[J]. Applied Mathematics and Mechanics, 2004, 25(8): 796-800.

Fan Xiu-chang. Using Generalized Variational Principles to Resolve the St. Venant’s Torsional Bar with a Crack[J]. Applied Mathematics and Mechanics, 1989, 10(2): 179-186.

Citation:

CHEN Fang-qi, LIANG Jian-shu, CHEN Yu-shu. Some Dynamical Behavior of the Stuart-Landau Equation With a Periodic Excitation[J]. Applied Mathematics and Mechanics, 2004, 25(8): 796-800.

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Some Dynamical Behavior of the Stuart-Landau Equation With a Periodic Excitation

1.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;

Received Date: 2003-01-16
Rev Recd Date: 2004-03-09
Publish Date: 2004-08-15

Abstract

Abstract

The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency were investigated in detail, respectively. The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.
- Stuart-Landau equation,
- bifurcation,
- universal unfolding,
- germ

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References(6)

References

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